Tate Britain's enormous pre-Raphaelite exhibition has 200 works – paintings, drawings, sculptures, wallpaper designs, embroidered bedspreads – and a single unifying theory. This is announced in the terse subtitle. The curators apparently want us to believe in the pre-Raphaelite brotherhood as Britain's first modern art movement, radical, difficult, rebellious, dangerously innovative and experimental. Why, even the bedspreads are avant garde.

This counterintuitive claim sounds like a case of Victorian humbug in itself. It wants to turn the pre-Raphaelites into proto-modernists, up there with the cubists or the abstract expressionists, even though their entire aesthetic is the most blatant and passionate denial of everything modern and 20th-century imaginable. It's a sensational argument, perhaps directed at a new young generation of gallery-goers. But it also feels like a faintly apologetic attempt to give the old boys a lift, casting their art as strange when it is the very definition of overfamiliarity.

For though this is the first Tate survey in almost 30 years, it never feels that way. The pre-Raphaelites are always with us. This show has all the classics you can see for free in our public museums, from Henry Wallis's dead Chattertonto Millais's Ophelia in her lush Surrey stream, from Holman Hunt's scapegoat cast out into the purple desert to his most popular period hit, The Light of the World(1851-56), with Christ appearing in satin, rubies and 24-carat halo against a seething twilight.

Painfully literal – Christ holds a big light – and laboriously allegoric, with its weeds, fallen apples and rusty door, against which Our Saviour knocks, this painting (in its many editions) was the Turin Shroud of the Victorian empire. Seven million people queued to see it from South Africa to New Zealand, some sinking to their knees in reverence. This is not avant-garde art, this is painting as moral and spiritual guidance.

Perhaps it's unfair to cite Holman Hunt in evidence against the show's argument. He is (to me) the least palatable of the pre-Raphaelites, the most didactic, sentimental and oppressive. His Shadow of Death, in which the young Christ, with alarmingly prominent veins, stretches his arms wide to throw a cruciform shadow over a rack of nails in his father's workshop, rams the point home so insistently it seems to resist appreciation altogether as art.

It's easier to contemplate the other pre-Raphaelites with modern eyes. There are the super-real details adored by the surrealists, and that heightened sense of the frozen moment that may have come from looking at early daguerreotypes. There are the sub-Freudian symbols and the weirdly suggestive shadows.

Millais's Ferdinand Lured by Ariel is so dreamlike in its excessive particularity it could have been made on LSD. Twenty different kinds of grass have been identified in its patch of meadow, and Ariel is not the standard Victorian fairy but a bizarre hermaphrodite buoyed up by cabbage-coloured bats. Burne-Jones's protagonists, with their faraway dark-ringed eyes, appear so transfixed they could be narcotised.

All of this is very well conveyed in the show, along with the inspiration the pre-Raphaelites found in medieval and renaissance art and – which is more of a revelation – the febrile visions of the 19th-century painter Theodor von Holst. Even the pre-Raphaelites' personal look (prolific sideburns, thick hanks of hair) turns out to have its origin in Germany's Nazarene painters, a band of pious primitivists who worshipped Dürer and wore their hair long in homage.

This is all abundantly clear from the pictures, as well as the texts. But the newer claims don't amount to very much. That Picasso admired an early Holman Hunt does not make the Victorian any more of a modern. That Kandinsky saw elements of abstraction in the work of Rossetti would surely have shocked the latter. Van Gogh may have admired Millais's Chill October – that still, sear threat of winter in a watery landscape that makes one cold all over – but the painting is hardly a classic brotherhood narrative.

Indeed, what this show really offers is not a new take on the pre-Raphaelites so much as the chance to be struck anew. For this is surely the oddest of art movements – obsessed with narrative, myth and fiction but addicted to pedantic fact; relentlessly symbolist and yet fanatically literal; contemporary in its preoccupation with prostitutes, workers, literacy, immigration and so on, yet with its roots in the medieval past.

Consider that this is a movement whose primary purpose was for everyone to paint in roughly the same way, in which the aesthetic was so programmatic that you could teach even a very mediocre brush-man such as William Morris to copy it. A movement intent on supplying its audience with visible models of virtue and vice, hope and despair, temptation and responsibility, where every picture tells a story but the moral is spelled out all over again for the slow of learning in labels within the painting and homilies lettered across the gilded frames.

This is an art that gives prominence to everything that can be researched – from the exact form of the stones outside Jerusalem to the pallor of a fading cornflower – but which gives the same weight to every single thing. An art in which nothing appears independent of the fact-checked precedent, in which there is no breath of life, no flexibility, no spontaneity.

These paintings could not be made – or viewed – in a hurry. A full-scale allegory such as William Shakespeare Burton's The Wounded Cavalier takes time to interpret, as you read your way from the expiring cavalier to the pack of fallen playing cards, the broken sword, the autumn tree and the red admiral alighting on the weapon at the dead centre of the painting. In the gloom stands a Puritan with a bible, looking down on this man who has lost his gamble. The Puritan is as upright as the tree trunk. Eight subscribers paid for this picture to be presented to the Corporation of London. It is painting as means of public address.

The Wounded Cavalier is something of a one-off because Burton invented the whole scenario, whereas most pre-Raphaelite costume dramas rely entirely on existing stories. Hamlet, Pygmalion, Lilith, The Lady of Shalott, even The Return of the Dove from the Ark – practically anything can be adjusted to accommodate the cataleptic damsels and drooping knights that infest this art.

Indeed, the curators' contention that this art is notable for its variety of approaches seems no more plausible at first than the avant-garde argument. But anyone prepared to make the effort to keep alert through room after room of densely crowded pictures will see that this is in some senses true.

Millais has a gift for visionary narrative anchored in extreme reality. He is the method painter par excellence (and so well represented here this amounts to a Millais show-within-a-show). Nobody is quite as weird as Rossetti and his monstrous regiment of women – all the same, even the so-called portraits of his wife – with their square jaws and centre partings, tumescent necks and vampire lips. And not even Holman Hunt, for all his electric lighting, is quite as artificial as Edward Burne-Jones, whose bloodless somnambulists are wandering about in some other world.

But although the paintings may differ from one artist to the next, what strikes is the deadening pre-Raphaelite effect. The characteristics are always the same: glistening excess, lurid colour, that all-over emphasis and oppressive density of detail that leaves the eye with nowhere to go, that demands your obedient attention. This is an art that insists on telling you where to look, what to think and how to feel – that wants to turn you into a passive Burne-Jones zombie.